According to wikipedia, airlines that fly to Kotoka International Airport in Accra Ghana are Alitalia, British Airways, Delta, EgyptAir, Emirates, KLM, Royal Air Maroc, Lufthansa. All of these should also have flights to Seattle, sometimes through codeshare with a partner (KLM cooperates with NorthWest).

http://en.wikipedia.org/wiki/Kotoka_International_Airport

If you try on the individual airlines' websites you'll definitely find flights to Accra from Seattle.

And you need to check date by date, you start by entering June 17th as departure and July 8th as return date. Then you change, try every possible combination of your dates.